Mysterious Weed

HELP! I’m unable to identify this weed. I spotted one growth a few years ago and now it took over 1/4 of our garden, it grows everywhere, even between stones (we have no grass) Any information would be much appreciated…

Day lilies*

Is it possible to get second bloom from day lilies. They always look so nice then when they are done it’s all just leaf.…

Daylillies*

I always thought that a registered daylily should look exactly like the photo on the AHS website for example and not have any “imperfections.” Is this true or am I expecting too much? Thanks in advance for your reply.…